I asked this question of an old friend of mine, Dr. Harry Cleghorn, who used to work for Alcoa, and he replied:
Regarding aluminum foil, 100 percent aluminum is extremely difficult to handle - it is very malleable, coats the iron rolls during hot and cold rolling and at foil gauges, it tears easily, generating a lot of scrap in the process.

By alloying with small amounts of Cu, Mn, Si, one produces the 2000 and 3000 - 3100 alloy series, which is the base stock for foil production. If my memory serves me correctly, the 2000 series is less often used for this purpose, but has the higher levels of Cu.

The alloying amounts are small, corresponding to about one-tenth of a percentage point in order of magnitude.

There are some historical footnotes regarding the first use of pure aluminum by the French aristocracy (the only people who could afford to use them) when spoons and forks would bend and be virtually useless when eating food! Scientists at the time found that the addition of copper and manganese helped to increase the tensile strength.